The SM and the Higgs Boson Daniele.Zanzi@cern.ch Is the Higgs boson - PowerPoint PPT Presentation

The SM and the Higgs Boson Daniele.Zanzi@cern.ch

Is the Higgs boson responsible for our mass?

Is the Higgs boson responsible for our mass? NO!!

How ordinary matter gets mass? Binding energy in nucleons 훥 p 훥 x ≥ h/2 휋 E=mc 2

Higgs field gives mass to elementary particles

Higgs field gives mass to elementary particles Does it matter for us?

Higgs field gives mass to elementary particles Does it matter for us?

Higgs field gives mass to elementary particles Can elementary particles have mass without the Higgs field?

Higgs field gives mass to elementary particles Can elementary particles have mass without the Higgs field? Yes…

QED Electron

QED Electron Mass term Kinetic term

QED Electron Mass term Kinetic term e L and e R have the same quantum numbers, so they Electron = + are different (chiral) states of the same particle left-handed e L right-handed e R

QED Electron Mass term Kinetic term e L and e R have the same quantum numbers, so they Electron = + are different (chiral) states of the same particle left-handed e L right-handed e R

QED Electron Mass term Kinetic term e L and e R have the same quantum numbers, so they Electron = + are different (chiral) states of the same particle left-handed e L right-handed e R Electron mass linked to the electron flipping between chiral states

Higgs field gives mass to elementary particles So, why we need the Higgs field?

Higgs field gives mass to elementary particles So, why we need the Higgs field? Because of symmetries in Nature…

Standard Model

Standard Model Interactions among particles driven by symmetries of Nature

Standard Model Interactions among particles driven by symmetries of Nature Classical mechanics: Symmetry in the system leads to conservation law (Noether’s theorem)

Standard Model Interactions among particles driven by symmetries of Nature Quantum mechanics: Symmetry in the system leads to charge conservation (quantized charges)

Standard Model Interactions among particles driven by symmetries of Nature Example: electrical charge conservation

Standard Model Interactions among particles driven by symmetries of Nature Global symmetry = charge conservation

Standard Model Interactions among particles driven by symmetries of Nature Local symmetry = FORCES Global symmetry Physics of the system unchanged if = points are ‘‘connected’’ by a field, charge conservation the gauge field

Standard Model SM characterized by the SU(3) ⨉ SU(2) L ⨉ U(1) Y gauge symmetry. (These symmetries are proven experimentally!)

Standard Model SM characterized by the strong force SU(3) ⨉ SU(2) L ⨉ U(1) Y gauge symmetry. (These symmetries are proven experimentally!)

Standard Model SM characterized by the SU(3) ⨉ SU(2) L ⨉ U(1) Y gauge e c r o f k a e w - o r symmetry. t c e e l (These symmetries are proven experimentally!)

Standard Model SM characterized by the SU(3) ⨉ SU(2) L ⨉ U(1) Y gauge symmetry. (These symmetries are proven experimentally!) So, why SM particles cannot have masses??

Standard Model SM characterized by the SU(3) ⨉ SU(2) L ⨉ U(1) Y gauge symmetry. (These symmetries are proven experimentally!) Electron = + left-handed e L right-handed e R

Standard Model SM characterized by the SU(3) ⨉ SU(2) L ⨉ U(1) Y gauge symmetry. (These symmetries are proven experimentally!) Electron = + left-handed e L right-handed e R Q -1 -1 Y -1 -2

Standard Model SM characterized by the SU(3) ⨉ SU(2) L ⨉ U(1) Y gauge symmetry. (These symmetries are proven experimentally!) Electron = + Y= -1 -2 -1 -2 left-handed e L right-handed e R Not allowed by hyper- Q -1 -1 charge conservation! Y -1 -2

Standard Model SM characterized by the SU(3) ⨉ SU(2) L ⨉ U(1) Y gauge symmetry. (These symmetries are proven experimentally!) Fermion mass terms are not allowed if the symmetries of SM are to be conserved. Same argument holds also for the masses of the gauge bosons. In this case the mass terms are not allowed by the preservation of the symmetry under gauge transformations. In a way, the gauge boson are the fields that ‘‘map’’ symmetries under local transformations. Since such transformations impact the entire system, these ‘‘’maps’’ need to have an infinite range, hence the carriers need to be massless

Here comes the Higgs field Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV)

Here comes the Higgs field Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) In the ground state (vacuum) the field is not null

Here comes the Higgs field Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) infinite degenerate ground states

Here comes the Higgs field Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value h (VEV) ζ two possible excitations (quanta): h requires energy ζ doesn’t cost energy

Here comes the Higgs field Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value h (VEV) ζ two possible excitations (quanta): h requires energy Any excitation is equally probable, ζ doesn’t cost energy ie the vacuum has an indefinite number of ζ quanta

Here comes the Higgs field Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value h (VEV) ζ two possible excitations (quanta): h requires energy Any excitation is equally probable, ζ doesn’t cost energy ie the vacuum has an indefinite number of ζ quanta Addition/subtraction of a ζ does not change the vacuum (see concept of condensate in superconductors)

Here comes the Higgs field Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value h (VEV) ζ Higgs field VEV ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ

Here comes the Higgs field Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value h (VEV) ζ Higgs field VEV ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ Y= -1 Y= -2

Here comes the Higgs field Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value h (VEV) ζ Higgs field VEV ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ Y= -1 ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ Y= -1 Y= -2

Here comes the Higgs field Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value h (VEV) ζ Higgs field VEV ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ Y= -1 ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ Y= -1 Y= -2

Here comes the Higgs field Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value h (VEV) ζ Higgs field VEV ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ Y= -1 ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ Y= -1 Y= -2

Here comes the Higgs field Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value h (VEV) ζ Higgs field VEV ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ Y= -1 ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ Electron acquires mass from the ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ interaction with the Higgs field! ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ Dynamic generation of mass that ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ preserves symmetries of SM ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ Y= -1 Y= -2

Here comes the Higgs field Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value h (VEV) ζ Also gauge bosons get mass interacting with Higgs field: Z Higgs field has weak 휙 ¡ ¡ charge, so it can emit a Z boson as electron radiates photons 휙 ¡ ¡